I have an intutive approach but I want to know why he work??I want proof??
suppose we will use the first 5 character..
first: we will put the the characters at even position like that:
`a_b_c_d_e_a_b_c_d_e_a_b_c_d_e`

the the first k chars at even positions we will shift them by 1
and put  the shifted chars at odd positions like that 
`a_b_c_d_e`
`_b_c_d_e_a`
`abbccddeea`

the second k chars at even positions we will shift them by 2
and put  the shifted chars at odd positions like that 
`a_b_c_d_e`
`_c_d_e_a_b`
`acbdcedaeb`

you can say that the char at odd position j is equal to the char at position (j-1) plus number of shifts like s[j]=(s[j-1]+sh)%k;
sorry for my bad english...can someone prove it??

here's my submision